Narrow Results

In this work, an explicit Taylor series expansion- and least square-based lattice Boltzmann method (LBM) is used to simulate two-dimensional unsteady incompressible viscous flows. The new method is based on the standard LBM with introduction of the Taylor series expansion and the least squares approach. The final equation is an explicit form and essentially has no limitation on mesh structure and lattice model. Since the Taylor series expansion is only applied in the spatial direction, the time accuracy of the new method is kept the same as the standard LBM, which seems to benefit for unsteady flow simulation. To validate the new method, two test problems, that is, the vortex shedding behind a circular cylinder at low Reynolds numbers and the oscillating flow in a lid driven cavity, were considered in this work. Numerical results obtained by the new method agree very well with available data in the literature.

The Taylor series expansion- and least squares-based lattice Boltzmann method (TLLBM) was used in this paper to extend the current thermal model to an arbitrary geometry so that it can be used to solve practical thermo-hydrodynamics in the incompressible limit. The new explicit method is based on the standard lattice Boltzmann method (LBM), Taylor series expansion and the least squares approach. The final formulation is an algebraic form and essentially has no limitation on the mesh structure and lattice model. Numerical simulations of natural convection in a square cavity on both uniform and nonuniform grids have been carried out. Favorable results were obtained and compared well with the benchmark data. It was found that, to get the same order of accuracy, the number of mesh points used on the nonuniform grid is much less than that used on the uniform grid.

The two-dimensional form of the Taylor series expansion- and least square-based lattice Boltzmann method (TLLBM) was recently presented by Shu et al.⁸ TLLBM is based on the standard lattice Boltzmann method (LBM), Taylor series expansion and the least square optimization. The final formulation is an algebraic form and essentially has no limitation on the mesh structure and lattice model. In this paper, TLLBM is extended to the three-dimensional case. The resultant form keeps the same features as the two-dimensional one. The present form is validated by its application to simulate the three-dimensional lid-driven cavity flow at Re=100, 400 and 1000. Very good agreement was achieved between the present results and those of Navier–Stokes solvers.

A new two-dimensional lattice kinetic scheme on the uniform mesh was recently proposed by Inamuro, based on the standard lattice Boltzmann method (LBM). Compared with the standard LBM, this scheme can easily implement the boundary condition and save computer memory. In order to remove the shortcoming of a relatively large viscosity at a high Reynolds number, a first-order derivative term is introduced in the equilibrium density distribution function. However, the parameter associated with the derivative term is very sensitive and was chosen in a narrow range for a high Reynolds number case. To avoid the use of the derivative term while removing the shortcoming of a relatively large viscosity, new lattice kinetic schemes are proposed in this work following the original lattice kinetic scheme. In these new lattice kinetic schemes, the derivative term is dropped out and the difficulty of the relatively large viscosity is eased by controlling the time step δt or sonic speed c_s. To validate these new lattice kinetic schemes, the numerical simulations of the two-dimensional square driven cavity flow at Reynolds numbers from 100 to 1000 are carried out. The results using the new lattice kinetic schemes are compared with the benchmark data.

An explicit Taylor series expansion and least square-based lattice Boltzmann method (TLLBM) is used to simulate the two-dimensional unsteady viscous incompressible flows. TLLBM is based on the well-known Taylor series expansion and the least square optimization. It has no limitation on mesh structure and lattice model. Its marching in time is accurate. Therefore, it is very suitable for simulation of time dependent problems. Numerical experiments are performed for simulation of flows past a rotational circular cylinder. Good agreement is achieved between the present results and available data in the literature.

In the past decades we have witnessed a paradigm-shift from scarcity of data to abundance of data. Big data and data analytics have fundamentally reshaped many areas including operations research. In this paper, we discuss how to integrate data with the model-based analysis in a controlled way. Specifically, we consider techniques to quantify input uncertainty and the decision making under input uncertainty. Numerical experiments demonstrate that different ways in decision making may lead to significantly different outcomes in a maintenance problem.

Chebyshev polynomial approximation is an effective method to study the stochastic bifurcation and chaos. However, due to irrational and fractional expressions existing in the denominator of some mechanical systems, the integral process is very complicated. The Taylor series expansion is proposed to expand the irrational and fractional expressions into a series of polynomials. Smooth and discontinuous oscillator was taken as an example, and the results show that the Taylor series expansion method is acceptable. The rub-impact force was taken as another example. Numerical results indicate that the method is suitable for the rub-impact rotor system.

The work reported in this paper explores holographic bounce. In the first phase of the study, we chose a non-singular bouncing scale factor. Then we reconstructed $f(T)$ gravity and analytically derived constraints on the bouncing parameter $\sigma$. These constraints helped us understand the scale factor’s quintessence or phantom behavior. Furthermore, we also explored the statefinder parameters for reconstructed $f(T)$ and observed the attainment of $\mathrm{\Lambda }$CDM fixed point. Next, we considered the multiplicative bouncing scale factor inspired by S. D. Odintsov and V. K. Oikonomou Phys. Rev. D 94, (2016) 064022. For this choice, we discussed the types of singularities realizable for different cases. Through the Talyor series expansion, we analytically presented cases and subcases for different ranges of $\alpha$ of the scale factor. In the last phase of the study, we demonstrated holographic bounce with the choice of the multiplicative scale factor. In this case, we considered holographic Ricci dark energy and Barrow holographic dark energy. We concluded that it is possible to generate constraints on the bouncing parameter for its feasibility for the EoS parameter. We concluded that the realization of holographic bounce is possible, and different suitable constraints can be derived for this multiplicative bouncing scale factor focusing on the realization of cosmic bounce.

Energy-momentum-dependent potentials corresponding to a separable nonlocal and a local potential are constructed to investigate nucleon-nucleus systems. With this interaction, the elastic phase shifts for the $\alpha$-n and $\alpha$-p collisions are calculated within the equivalent potential model. Without further adjustment, a good agreement with experimental data is obtained with a small model space. Additionally, the scattering cross-sections are computed using the partial wave phase parameters.

Dual-arm robotic manipulators are used in industry and for assisting humans since they enable dexterous handling of objects and more agile and secure execution of pick-and-place, grasping or assembling tasks. In this paper, a nonlinear optimal control approach is proposed for the dynamic model of a dual robotic arm. In the considered application, the dual-arm robotic system has to transfer an object under synchronized motion of its two end-effectors so as to achieve precise positioning and to compensate for contact forces. The dynamic model of this robotic system is formulated while it is proven that the state-space description of the robot’s dynamics is differentially flat. Next, to solve the associated nonlinear optimal control problem, the dynamic model of the dual-arm robot undergoes approximate linearization around a temporary operating point that is recomputed at each time-step of the control method. The linearization relies on Taylor series expansion and on the associated Jacobian matrices. For the linearized state-space model of the dual-arm robot, a stabilizing optimal (H-infinity) feedback controller is designed. This controller stands for the solution to the nonlinear optimal control problem under model uncertainty and external perturbations. To compute the controller’s feedback gains an algebraic Riccati equation is repetitively solved at each iteration of the control algorithm. The stability properties of the control method are proven through Lyapunov analysis. The proposed nonlinear optimal control approach achieves fast and accurate tracking of reference setpoints under moderate variations of the control inputs.

A package solution is presented for the full-scale bounds estimation of temperature in the nonlinear transient heat transfer problems with small or large uncertainties. When the interval scale is relatively small, an efficient Taylor series expansion-based bounds estimation of temperature is stressed on the acquirement of first and second-order derivatives of temperature with high fidelity. When the interval scale is relatively large, an optimization-based approach in conjunction with a dimension-adaptive sparse grid (DSG) surrogate is developed for the bounds estimation of temperature, and the heavy computational burden of repeated deterministic solutions of nonlinear transient heat transfer problems can be efficiently alleviated by the DSG surrogate. A temporally piecewise adaptive algorithm with high fidelity is employed to gain the deterministic solution of temperature, and is further developed for recursive adaptive computing of the first and second-order derivatives of temperature. Therefore, the implementation of Taylor series expansion and the construction of DSG surrogate are underpinned by a reliable numerical platform. The parallelization is utilized for the construction of DSG surrogate for further acceleration. The accuracy and efficiency of the proposed approaches are demonstrated by two numerical examples.

Attitude control and stabilization of micro-satellites is a nontrivial problem due to the highly nonlinear and multivariable structure of the satellites’ state-space model. In this paper, a novel nonlinear optimal (H-infinity) control approach is developed for this control problem. The dynamic model of the satellite’s attitude dynamics undergoes first approximate linearization around a temporary operating point which is updated at each iteration of the control algorithm. The linearization process relies on first-order Taylor series expansion and on the computation of the Jacobian matrices of the state-space model of the satellite’s attitude dynamics. For the approximately linearized description of the satellite’s attitude a stabilizing H-infinity feedback controller is designed. To compute the controller’s feedback gains, an algebraic Riccati equation is solved at each time-step of the control method. The stability properties of the control scheme are proven through Lyapunov analysis. It is also demonstrated that the control method retains the advantages of linear optimal control that is fast and accurate tracking of the reference setpoints under moderate variations of the control inputs.

Free-floating space robotic manipulators (FSRMs) are robotic arms mounted on space platforms, such as spacecraft or satellites which are used for the repair of space vehicles or the removal of noncooperating targets such as inactive material remaining in orbit. In this paper, a novel nonlinear optimal control method is applied to the dynamic model of FSRMs. First, the state-space model of a 3-DOF free-floating space robot is formulated and its differential flatness properties are proven. This model undergoes approximate linearization around a temporary operating point that is recomputed at each time-step of the control method. The linearization relies on Taylor series expansion and on the associated Jacobian matrices. For the linearized state-space model of the free-floating space robot a stabilizing optimal (H-infinity) feedback controller is designed. This controller stands for the solution of the nonlinear optimal control problem under model uncertainty and external perturbations. To compute the controller’s feedback gains an algebraic Riccati equation is repetitively solved at each iteration of the control algorithm. The stability properties of the control method are proven through Lyapunov analysis. The proposed nonlinear optimal control approach achieves fast and accurate tracking of setpoints under moderate variations of the control inputs and a minimum dispersion of energy by the actuators of the free-floating space robot.